1,720,988 research outputs found
Stability for delayed reaction-diffusion neural networks
No full textWe consider a Hopfield neural network model with diffusive terms, non-decreasing and discontinuous neural activation functions, time-dependent delays and time-periodic coefficients. We provide conditions on interconnection matrices and delays which guarantee that for each periodic input the model has a unique periodic solution that is globally exponentially stable. Even in the case without diffusion, such conditions improve recent results on classical delayed Hopfield neural networks with discontinuous activation functions. Numerical examples illustrate the results
Existence and optimal control for periodic parabolic equations with nonlocal terms
No full textMotivated by models which have been proposed for some problems in mathematical biology and fisheries management and elsewhere, we consider a nonlinear periodic parabolic problem and an associated cost functional J. A key feature of our problem is the presence of a nonlocal term which—as we show by direct example—renders the standard mono-tonicity methods invalid. We therefore employ topological methods to deal both with existence of solutions and of minima of J over the Control set. Some considerations are also presented on related systems and on the question of uniqueness
Periodic solutions to nonlinear equations with oblique boundary conditions
Full text linkWe study the existence of positive periodic solutions to nonlinear elliptic and parabolic equations with oblique and dynamical boundary conditions and non-local terms. The results are obtained through fixed point theory, topological degree methods and properties of related linear elliptic problems with natural boundary conditions and possibly nonsymmetric principal part. As immediate consequences, we also obtain estimates on the principal eigenvalue for non-symmetric elliptic eigenvalue problems. © 2012 Juliusz Schauder University Centre for Nonlinear Studies
Common asymptotic behavior of solutions and almost periodicity for discontinuous, delayed, and impulsive neural networks
No full textThe paper considers a general neural network model with impulses at a given sequence of instants, discontinuous neuron activations, delays, and time-varying data and inputs. It is shown that when the neuron interconnections satisfy an M-matrix condition, or a dominance condition, then the state solutions and the output solutions display a common asymptotic behavior as time t → +∞. It is also shown, via a new technique based on prolonging the solutions of the delayed neural network to −∞, that it is possible to select a unique special solution that is globally exponentially stable and can be considered as the unique global attractor for the network. Finally, this paper shows that for almost periodic data and inputs the selected solution is almost periodic; moreover, it is robust with respect to a large class of perturbations of the data. Analogous results also hold for periodic data and inputs. A by-product of the analysis is that a sequence of almost periodic impulses is able to induce in the generic case (nonstationary) almost periodic solutions in an otherwise globally convergent nonimpulsive neural network. To the authors’ knowledge the results in this paper are the only available results on global exponential stability of the unique periodic or almost periodic solution for a general neural network model combining three main features, i.e., impulses, discontinuous neuron activations and delays. The results in this paper are compared with several results in the literature dealing with periodicity or almost periodicity of some subclasses of the neural network model here considered and some hints for future work are given
Analysis of a lagoon ecological model with anoxic crises and impulsive harvesting
Full text linkWe analyze mathematically a system of impulsive nonlinear parabolic equations that model a shallow lagoon subject to anoxic crises and two types of impulsive harvesting. The main focus is on the existence and properties of periodic solutions. In particular we give conditions that ensure the existence of such solutions and examine the effect of harvesting on the occurrence of anoxic crises. Our approach is based on estimates of the principal eigenvalue of associated linear problems, and on results from Nonlinear Functional Analysis. In particular, we obtain explicit criteria that involve the integrals of coefficients rather than maxima and minima. This is significant due to the large seasonal variations in the coefficient values
Positive solutions of elliptic non-positone problems
No full textWe give conditions for the existence or nonexistence of positive solutions of second-order subcritical elliptic nonpositone problems. We do not assume that the problems are radial, nor that they satisfy a variational structure. Our chief tools are Degree Theory, a priori estimates, and Maximum Principle arguments. © 1992, Khayyam Publishing. All rights reserved
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